In U.S. Pat. No. 3,990,005, commonly assigned to the present assignee, and incorporated herein by reference, there is disclosed a system for capcitively gauging the thickness, typically of a semiconductor wafer, utilizing two distance gauging probes placed on opposing sides of the wafer. The disclosure there provides a means for establishing an accurate measure of thickness, or other properties, in the case where the semiconductor wafer is either ungrounded or of such resistance to ground that the potential of the wafer is not controllable, resulting from error in the measurement. In one embodiment, the source of error from an ungrounded wafer is compensated by applying alternating current excitation to the probes in phase opposition which, where the wafer is substantially centered between the probes, avoids this error source.
An additional error source will be present dependent upon the displacement of the wafer from the centered condition and such error will have a relationship to the off centered position which is radically nonlinear, having error terms of a higher order than a linear relationship, typically being quadratic.
The present invention provides a system for compensating for that off-center error by processing the probe output signals in a manner to develop an offset error compensating signal which is combined with the probe output in such manner as to substantially reduce higher order error components in the thickness signal, as a function of the off-center position.
While the invention finds particular application in the semiconductor thickness gauging field for compensating for error in the wafer offset position it is additionally useful in other environments where a plurality of distance measuring probes are spaced from an object and where the resulting probe output signals are combined in such manner that an error function reflective of differences in probe spacing from the object from a nominal, typically equal distance, generates higher order error functions.